S2T1 Table 1: Accuracy without Validation footnote4 The authors in [lim2021new] did not name this homophily metric. We name it class homophily based on its definition. From the performance comparison on semi-supervised node classification tasks with different label percentage in table S2T1, we can see that the proposed models consistently perform better than the state-of-the-art models, especially when there are less labeled nodes. See detailed experimental results in [luan2019break]. The performance of SGC-1 and GCN are expected to be monotonically increasing with a proper and informative homophily metric. However, Figure S3F13(a)(b)(c) show that the performance curves under Hedge(G),Hnode(G) and Hclass(G) are U-shaped footnote5 , while Figure S3F13(d) reveals a nearly monotonic curve only with a little numerical perturbation around 1. Besides the 9 benchmark datasets Cornell, Wisconsin, Texas, Film, Chameleon, Squirrel, Cora, Citeseer and Pubmed used in [pei2020geom], we further test the above models on a new benchmark dataset, Deezer-Europe, that is proposed in [lim2021new]. On each dataset used in [pei2020geom], we test the models 10 times following the same early stopping strategy, the same random data splitting method and Adam [kingma2014adam] optimizer as used in GPRGNN [chien2021adaptive]. For Deezer-Europe, we test the above models 5 times with the same early stopping strategy, the same fixed splits and AdamW [loshchilov2017decoupled] used in [lim2021new].

On Addressing the Limitations of Graph Neural Networks

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